# The Dehn functions of Stallings–Bieri groups

@article{Carter2015TheDF, title={The Dehn functions of Stallings–Bieri groups}, author={William Carter and Max Forester}, journal={Mathematische Annalen}, year={2015}, volume={368}, pages={671-683} }

We show that the Stallings–Bieri groups, along with certain other Bestvina–Brady groups, have quadratic Dehn function.

## 9 Citations

### Identifying Dehn functions of Bestvina–Brady groups from their defining graphs

- Mathematics
- 2021

Let $$\Gamma $$
be a finite simplicial graph such that the flag complex on $$\Gamma $$
is a 2-dimensional triangulated disk. We show that with some assumptions, the Dehn function of the associated…

### Dehn Functions of Bestvina-Brady Groups

- Mathematics
- 2019

In this dissertation, we prove that if the flag complex on a finite simplicial graph is a 2-dimensional triangulated disk, then the Dehn function of the associated Bestvina–Brady group depends on the…

### Dehn functions of coabelian subgroups of direct products of groups

- Mathematics
- 2021

We develop new methods for computing the precise Dehn functions of coabelian subgroups of direct products of groups, that is, subgroups which arise as kernels of homomorphisms from the direct product…

### Separating automatic from Cayley automatic groups

- Mathematics
- 2020

We investigate the problem of distinguishing non-automatic Cayley automatic groups from automatic groups. It is well known that automatic groups are finitely presented with either linear or quadratic…

### Cohomological and Metric Properties of Groups of Homeomorphisms of R

- MathematicsOberwolfach Reports
- 2019

In recent years, the family of groups sharing features or design principles with classical Thompson groups has grown considerably. The workshop highlights new developments in this field with special…

### Residually free groups do not admit a uniform polynomial isoperimetric function

- MathematicsProceedings of the American Mathematical Society
- 2020

We show that there is no uniform polynomial isoperimetric function for finitely presented subgroups of direct products of free groups, by producing a sequence of subgroups $G_r\leq F_2^{(1)} \times…

### On the geometry of Cayley automatic groups

- MathematicsInt. J. Algebra Comput.
- 2022

In contrast to being automatic, being Cayley automatic a priori has no geometric consequences. Specifically, Cayley graphs of automatic groups enjoy a fellow traveler property. Here, we study a…

### Encoding and detecting properties in finitely presented groups

- Mathematics
- 2017

In this thesis we study several properties of finitely presented groups, through the unifying paradigm of encoding sought-after group properties into presentations and detecting group properties from…

### Bestvina--Brady Groups with Polynomial Dehn Functions

- Mathematics
- 2019

Let $\Gamma$ be a finite simplicial graph that contains no induced $K_{4}$ subgraphs. We show that with some assumptions, the Dehn function of the associated Bestvina--Brady group is polynomial.

## References

SHOWING 1-10 OF 21 REFERENCES

### The Dehn Function of Stallings’ Group

- Mathematics
- 2009

We prove that the Dehn function of a group of Stallings that is finitely presented but not of type $${\mathcal{F}_3}$$ is quadratic.

### Doubles, Finiteness Properties of Groups, and Quadratic Isoperimetric Inequalities☆☆☆

- Mathematics
- 1999

Abstract We describe a doubling construction that gives many new examples of groups that satisfy a quadratic isoperimetric inequality. Using this construction, we prove that the presence of a…

### An isoperimetric function for Bestvina–Brady groups

- Mathematics
- 2007

Given a right‐angled Artin group A, the associated Bestvina–Brady group is defined to be the kernel of the homomorphism A → ℤ that maps each generator in the standard presentation of A to a fixed…

### Finitely Presented Subgroups of Automatic Groups and their Isoperimetric Functions

- Mathematics
- 1996

We describe a general technique for embedding certain amalgamated products into direct products. This technique provides us with a way of constructing a host of finitely presented subgroups of…

### The geometry and topology of Coxeter groups

- Philosophy
- 2008

These notes are intended as an introduction to the theory of Coxeter groups. They closely follow my talk in the Lectures on Modern Mathematics Series at the Mathematical Sciences Center in Tsinghua…

### The Dehn function of SL(n;Z)

- Mathematics
- 2009

We prove that when n >= 5, the Dehn function of SL(n;Z) is quadratic. The proof involves decomposing a disc in SL(n;R)/SO(n) into triangles of varying sizes. By mapping these triangles into SL(n;Z)…

### The Geometry of the Word Problem for Finitely Generated Groups

- Mathematics
- 2007

Dehn Functions and Non-Positive Curvature.- The Isoperimetric Spectrum.- Dehn Functions of Subgroups of CAT(0) Groups.- Filling Functions.- Filling Functions.- Relationships Between Filling…

### Pushing fillings in right‐angled Artin groups

- MathematicsJ. Lond. Math. Soc.
- 2013

The results give sharp bounds on the higher Dehn func- tions of Bestvina-Brady groups, a complete characterization of the divergence of geodesics in RAAGs, and an upper bound for filling loops at infinity in the mapping class group.